Turbine stage

ABSTRACT

A turbine stage which has a stationary blade set (204) followed by a moving blade set (205) which have blades (206, 207) mounted between a floor plate (201, 211) and a ceiling plate (202, 212). 
     The surfaces of the ceiling plate (202, 212) and/or of the floor plate (201, 211) have as their meridian lines sinusoids with the maximum for the ceiling plate (202, 211) and the maximum or the minimum for the floor plate (201, 211) located in the plane between the blade sets. The curvature of the sinusoid at the outlet end. 
     The curvature of the sinusoid at the outlet end of the stationary blade set (204) is calculated so as to make the tangential static pressure gradient equal to the radial static pressure gradient at the ceiling plate and/or at the floor plate equal at the outlet end of the stationary blade set (204). 
     The disturbances are confined to restricted zones and the efficiency of the stage is thereby improved.

FIELD OF THE INVENTION

The present invention relates to a turbine stage which has a stationarycircular blade set followed by a moving circular blade set, each sethaving blades assembled between a floor plate and ceiling plate.

The succession of blades thus formed therefore defines a group ofpassages along which a fluid flows, each passage being delimited by twoconsecutive blades and by the floor plate and the ceiling plate.

BACKGROUND OF THE INVENTION

It is known that in a given passage, at points which are sufficientlyfar from the walls of the passage, the stream lines follow paths whichare substantially parallel to the walls of the passage formed by theconcave and convex surfaces of the blades.

At all points along the path, the centrifugal force which is exerted ona particle is balanced by the pressure forces. The result of this is,generally, that the concave surface of the blade is subjected to ahigher pressure than is the convex surface.

It is also known that in the boundary layer near the floor plate andceiling plate, the speed of the fluid is low. It follows that since thepressure forces are no longer balanced, the stream lines are curvesperpendicular to the isobars and follow paths of considerable slippagein each passage from the concave surface to the convex surface as iswell known to the person skilled in the art (FIG. 1).

The slippage generates a counterclockwise eddy against the ceiling plateof the passage and a clockwise eddy against the floor plate as seen byan observer placed downstream from the set of blades of FIG. 1.

These disturbances cause important losses known as secondary losses andthe smaller the ratio between the height of the blades and the chord,the more the efficiency of a set of blades is reduced.

It has been observed that in the case of a stationary circular set ofblades, the effect of the radial static pressure gradient which developsat the outlet end when the meridian line of flow is cylindrical, conicalor slightly curved adds to the phenomenon described hereinabove.

This gradient results from the centrifugal acceleration due to theperipheral component of the absolute speed at the outlet end of theblade set and increases the secondary eddy at the upper contour of theflow stream and reduces it at the lower contour thereof (FIG. 2) sincethe static pressure increases radially from the bottom of the blade setto the top of the blade set.

The variation in the static pressure in the plane between blades sets asa function of the radius is as shown in FIG. 3.

The slope of the curve at the bottom and at the top is equal to:##EQU1## p . . . Static pressure in the plane between blade sets. r . .. Radius.

ρ . . . Density of the fluid.

V_(u) . . . Tangential component of the absolute fluid speed in theplane between blade sets.

The direction of radial variation of the static pressure which decreasesfrom the ceiling plate to the floor plate simplifies the secondary eddyat the ceiling plate and opposes the secondary eddy at the floor plate,as illustrated in FIG. 2.

In the conventional case of a passage with a floor plate and a ceilingplate, the radial gradient of the static pressure in the plane betweenblade sets is detrimental at the ceiling plate and favourable at thefloor plate. This does not mean, however, that the absolute value of theradial gradient of the static pressure at the floor plate is the bestfor minimizing the secondary losses.

The invention relates to a turbine stage with a circular stationaryblade set followed by a circular moving blade set, each blade set havingblades mounted between a floor plate and a ceiling plate which areradially symmetrical about a turbine shaft, the pitch of the stationaryblades being L_(S) at the ceiling plate and L_(B) at the floor plate andthe outlet angle of the stream of fluid from the stationary blade setrelative to the plane between said blade sets being α1_(S) adjacent tothe ceiling plate and α1_(B) adjacent to the floor plate, in which stagethe distance between the turbine shaft and the surface of the ceilingplate decreases when going from the inlet end of the stationary bladeset to the outlet end of the stationary blade set where its value isr_(S) and then increases going from the inlet end of the moving bladeset where its value is r_(S) up to the outlet end of the moving bladeset.

Such a turbine stage is disclosed in British Pat. No. 596 784.

In the stage described in said British patent, the curve of the floorplate and of the ceiling plate is calculated to provide constantpressure in the plane between the blades sets (at the outlet end of thestationary blade set) from the top to the bottom of said space, i.e. theradial static pressure gradient is zero.

In the turbine stage in accordance with the invention, the central curveof the ceiling plate at the plane between the blade sets issubstantially equal to ##EQU2##

Thus, in the neighbourhood of the ceiling plate, the radial staticpressure gradient is equal to the tangential static pressure gradientbetween the blades sets. This confines the disturbed zone at the ceilingplate to a relatively small flow cross-section.

This invention also relates to a turbine stage with a circularstationary blade set followed by a circular moving blade set havingblades mounted between a floor plate and a ceiling plate which areradially symmetrical about a turbine shaft, the pitch of the stationaryblades being L_(S) at the ceiling plate and L_(B) at the floor plate andthe outlet angle of the stream of fluid from the stationary blade setrelative to the plane between said blade sets being α1_(S) adjacent tothe ceiling plate and α1_(B) adjacent to the floor plate, in which stagethe distance between the turbine shaft and the surface of the floorplate varies continuously from the inlet end of the stationary blade setto the outlet end of said stationary blade set where it reaches aextreme value r_(B) then varies continuously in the opposite directionfrom the inlet of the moving blade set where its value is r_(B) up tothe outlet of the moving blade set.

Said turbine stage is also described in British Pat. No. 596 784.

SUMMARY OF THE INVENTION

In the turbine stage in accordance with the invention, the central curveof the floor plate of the stationary blade set at the plane between theblade sets is substantially equal to the difference ##EQU3## the extremevalue r_(B) being a minimum when the difference is negative and amaximum when the difference is positive.

Therefore, in the neighbourhood of the floor plate, the radial staticpressure gradient in the plane between the blade sets is not zero as itis in the British patent, but is equal to the tangential static pressuregradient in the plane between the blade sets. This confines thedisturbed zone at the floor plate to a relatively small flowcross-section.

Obviously, in accordance with the invention the shape at the ceilingplate can be combined with the shape at the floor plate so as to confinethe disturbed zone at both the ceiling plate and at the floor plate torelatively small flow cross-sections.

According to a first variant of the invention, when means are providedto reduce the tangential static pressure gradient in the neighbourhoodof the ceiling plate at the outlet end of the stationary blade set by afactor λ(λ>1) and the curvature of the meridian line of the ceilingplate of the stationary blade set perpendicular to the plane between theblade sets is substantially equal to ##EQU4##

Therefore, in the neighbourhood of the ceiling plate, at the outlet endof the stationary set of blades, the radial static pressure gradient iskept equal to the tangential static pressure.

According to a second variant of the invention, when means are providedto reduce the tangential static pressure gradient in the neighbourhoodof the floor plate at the outlet end of the stationary blade set by afactor λ'(λ'>1) and the curvature of the meridian line of the floorplate of the stationary blade set perpendicular to the plane between theblade sets is substantially equal to ##EQU5## the extreme value r_(B)being a minimum when the difference is negative and a maximum when thedifference is positive. Therefore, in the neighbourhood of the floorplate, at the outlet end of the stationary blade set, the radial staticpressure gradient is kept equal to the tangential static pressure.

In accordance with a preferred embodiment of the invention these twovariants of the turbine stage are combined. This allows firstly theintensity of the eddies at the ceiling and floor plates to be reducedand secondly the eddies to be confined to a narrow zone.

Preferably, the distance between the turbine shaft and the surface ofthe ceiling plate of the stationary blade set varies in a curve whichhas a maximum at the inlet end of the stationary blade set and at theoutlet and of the moving blade set and a minimum in the plane betweenthe blade sets.

Likewise, the distance which separates the turbine shaft from thesurface of the floor plate follows a curve which has:

either a maximum in the plane between the sets of blades which maximumis associated with a minimum at the inlet end of the stationary bladeset and at the outlet end of the moving blade set;

or a minimum in the plane between the blade sets which minimum isassociated with a maximum at the inlet end of the stationary blade setand at the outlet end of the moving blade set.

However, manufacture can be facilitated by replacing the curved meridianlines of the ceiling and/or floor plates of the moving blade set bystraight line segments.

Embodiments of the present invention are described by way of examplewith reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1 and 2 illustrate part of a stationary blade set of aconventional turbine stage.

FIG. 3 illustrates the curves of pressure variation in the plane betweenthe blade sets as a function of distance r from the shaft.

FIG. 4 schematically illustrates a set of stationary blades of a turbinestage in accordance with the invention.

FIG. 5 illustrates a cross-section at the ceiling plate of a set ofstationary turbine blades according to FIG. 4.

FIG. 6 illustrates a cross-section at the floor plate of a stationaryblade set according to FIG. 4.

FIG. 7 illustrates a first embodiment of a turbine stage in accordancewith the invention.

FIG. 8 illustrates a second embodiment of a turbine stage in accordancewith the invention.

FIG. 9 illustrates a third embodiment of a turbine stage in accordancewith the invention.

FIG. 10 illustrates a fourth embodiment of a turbine stage in accordancewith the invention.

FIG. 11 illustrates a fifth embodiment of a turbine stage in accordancewith the invention.

FIGS. 12 and 13 illustrate simplified versions of the embodiment ofFIGS. 10 and 11.

FIGS. 14 and 15 illustrates a modified turbine still in accordance withthe invention which turbine has means to reduce the tangential staticpressure gradient of a stationary blade set.

DESCRIPTION OF PREFERRED EMBODIMENTS

In FIG. 1, two blades A and B form part of a stationary set of blades.Their roots are fixed to a floor plate 1 and their heads are fixed to aceiling plate 2. Said floor and ceiling plates are usually co-axial,cylindrical or frustoconical members.

The concave surface of the blade B, the convex surface of the blade A,the floor plate 1 and the ceiling plate 2 define a passage 3.

Fluid far from the walls of the passage flows smoothly along streamlinessuch as (c). In contrast, stream lines of fluid which come into contactwith the ceiling plate and the floor plate are orthogonal to the isobarsand flow in the directions shown (l) and (m), then begin to be turbulentas soon as they strike the convex surface of the blade (A).

FIG. 2 shows the static pressure at the outlet from the stationary setof blades. In the neighbourhood of the ceiling plate the static pressureis p_(S) and in the neighbourhood of the floor plate it is p_(B).

The pressure p_(S) is higher than the pressure p_(B) so that in theneighbourhood of the ceiling plate, the secondary turbulence isamplified while it is damped in the neighourhood of the floor plate.

The static pressure decreases constantly from the ceiling plate to thefloor plate.

The radial static pressure between adjacent blade sets in a conventionalturbine is shown schematically in FIG. 3 by the solid-line curve whichgoes from r_(B) representing the radius of the floor plate in the planebetween the blade sets to r_(S) representing the radius of the ceilingplate in the same plane. The dashed line shows the desired curve.

FIG. 4 shows the result to be obtained at the outlet end of a stationaryblade set.

To confine the disturbed zone to a relatively small flow pathcross-section at the ceiling plate and/or at the floor plate it isnecessary to equalize the absolute values of the tangential staticpressure gradient (dp/dt) and of the radial static pressure gradient(dp/dr) at the ceiling plate and/or at the floor plate at the outlet endof the stationary blade set.

Therefore, arrangements must be made such that, at the ceiling plate.##EQU6## while at the floor plate ##EQU7## from the floor plate to theceiling plate ##EQU8## from the ceiling plate to the floor plate.

To produce this effect, the meridian line of the ceiling plate and/or ofthe floor plate of the stationary blade set must be curved in a radialplane.

FIG. 5 is a cylindrical cross-section through the tops of blades A and Bof a stationary blade set.

Angle α_(1S) is the stream injection angle (into the following movingblade set) relative to the blade tip line on the ceiling plate; V₁ isthe absolute speed between the blade sets; V_(u) is the tangentialcomponent of the absolute speed between the blade sets; and V_(m) is theaxial component of the absolute speed between the blade sets in themeridian plane.

L_(S) is the pitch of the blades at the ceiling plate; the angle α_(1S)can very easily be calculated from the equation ##EQU9## (δ_(S) beingthe width of the constriction between the blades A and B in theneighbourhood of the ceiling plate).

FIG. 6 is a cylindrical cross-section through the roots of blades A andB of a stationary blade set.

Angle α_(1B) is the stream injection angle (into the following movingblade set) relative to the exit plane of the stationary blade set.

The pitch of the blades A and B at the floor plate is L_(B) ; the widthof the contriction is δ_(B) ; the angle α_(1B) can very easily becalculated from the equation ##EQU10##

Here, now, are the calculations of the radii of curvature to be impartedto the curved meridian lines of the ceiling and floor plates at theoutlet from the stationary blade set (i.e. in the plane between theblade sets).

The radial static pressure gradient between the blade sets is determinedby the following equation: ##EQU11## where V_(m) is the absolute speedbetween the blades in the meridian plane and 1/R is the curvature of themeridian fluid stream lines.

p, r, δ and V_(u) have the same meanings as in equation (1).

R is negative in equation (2) when the meridian lines deviate towardsthe turbine shaft; otherwise R is positive.

Now, it is known that ##EQU12## where α₁ is the injection angle of thefluid stream relative to the plane between blade sets at radius r and Lis the spacing between two consecutive blades at the same radius.

1/2 is an experimental coefficient and

ΔP is the pressure drop in the stationary blade set.

Now, in accordance with Bernouilli's theorem

    ΔP=1/2ρV.sub.1.sup.2                             (4)

Also,

    V.sub.1.sup.2 =V.sub.u.sup.2 +V.sub.m.sup.2                (5)

By making the value of |dp/dr| equal to that of |dp/dt| we find##EQU13## with the sign (+) in the case of the floor plate and the sign(-) in the case of the ceiling plate, dividing through by ρV_(m) ², weget ##EQU14## and since ##EQU15##

FIG. 7 is a cross-section through a turbine stage in accordance with theinvention in which stage the effect of the secondary losses is minimizedin the neighbourhood of the ceiling plate. The fluid, e.g. steam, flowsfrom right to left in the direction of the arrow.

The stage has a stationary blade set 4 followed by a moving blade set 5.

The stationary blade set has blades 6 assembled between a floor plate 1and a ceiling plate 2.

The moving plate set 5 has blades 7 assembled between a floor plate 11and a ceiling plate 12.

The ceiling plate 2 of the stationary blade set 4 is a body ofrevolution about the turbine axis and its meridian line follows one halfof a cycle of a sinusoid which gets nearer to the turbine axis whengoing from the inlet end to the outlet end of the stationary blade set4.

The ceiling plate 12 of the moving blade set 5 is substantiallysymmetrical to the ceiling plate 2 relative to the plane between bladesets which is perpendicular to the turbine axis.

The curvature of the meridian line of the ceiling plate in the planebetween blade sets is ##EQU16##

Instead of being in the form of half a cycle of a sinusoid, the meridianline of the ceiling plate 12 could be in the form of an inclined segmentof a straight line sloping away from the axis when going from the inletend to the moving blade set 5, (where the ceiling plate 12 is r_(S)distant from the turbine axis) towards the outlet end thereof.

In the embodiment illustrated in FIG. 7, the floor plate is that of aconventional turbine.

FIGS. 8 and 9 are a cross-sections through turbine stages in accordancewith the invention in which the effect of the secondary losses in theneighbourhood of the floor plate is minimized.

The reference numerals are the same as for FIG. 7 but with 100 added toeach reference.

In the case of FIG. 8, the floor plate 101 of the stationary blade set104 is a body of revolution about the turbine axis and its meridian lineis a half cycle of a sinusoid which slopes towards the turbine axis whengoing from the inlet towards the outlet.

The floor plate 111 of the moving blade set 105 is substantiallysymmetrical to the lower plate 101 relative to the plane between bladesets.

As in the case of FIG. 7, the sinusoidal shape of the meridian line ofthe floor plate 111 could be replaced by an inclined straight linesloping away from the turbine axis when going from the inlet end (whereit is r_(B) distant from the turbine axis) towards the outlet end of themoving blade set 105.

The curvature of the floor plate in the plane between blade sets is##EQU17## In FIG. 9 the difference between ##EQU18## is positive becausethe meridian line of the floor plate 101' of the stationary blade set104 is in the form of half a cycle of a sinusoid which slopes away fromthe axis when going from the inlet end towards the outlet end of theblade set.

The meridian line of the floor plate 111' of the moving blade set 105 issymmetrical to the meridian line of the floor plate 101' relative to theplane between blade sets. A meridian line could also be constituted by asegment of a straight line sloping towards the turbine axis going fromthe inlet end (where it is r_(B) distant from the axis) to the outletend of the moving blade set 105.

The curvature in the plane between blade sets at the floor plate istherefore equal to ##EQU19##

FIG. 10 illustrates a turbine stage in accordance with the inventionwith a ceiling plate similar to that of the turbine stage in FIG. 7 anda floor plate similar to that of FIG. 8. The reference numerals have 200added to corresponding numerals of FIG. 7.

Likewise, FIG. 11 illustrates a turbine stage in accordance with theinvention with a ceiling plate like that of the turbine stage of FIG. 7and a floor plate like that in FIG. 9. The reference numerals have 300added to corresponding numerals of FIG. 7.

FIGS. 12 and 13 are variants of FIGS. 10 and 11 in which variants themeridian lines of the floor plates 311 and 311' respectively and of theceiling plate 312 of the moving blade set 305 are straight lines.

FIG. 14 is a cross-section through a stationary blade set taken in acylindrical surface about the turbine axis, said blade set includingmeans for reducing secondary losses in each of the passages delimited bythe convex surface 401 of one blade A and the concave surface 402 of anadjacent blade B. These means are described for example in Belgian Pat.No. 677 969. The floor plate and/or the ceiling plate are hollowed outin the neighbourhood of the convex surface of the blade A (see reference403). This locally reduces excess pressure perpendicular to the floorplate and/or to the ceiling plate.

Similarly, matter is added at 401 to the floor plate and/or the ceilingplate in the neighbourhood of the concave surface of the blade B. Thislocally reduces the pressure perpendicular to the floor plate and/or tothe ceiling plate.

This causes a reduction in the pressure difference between the concavesurface and the convex surface and therefore reduces the secondarylosses.

The inside shape of the stationary blade set also has a periodicity2π/N_(D) radians where N_(D) is the number of blades in the guide vane.However, in the outlet end plane of the blade set perpendicular to theturbine axis, the set of passages is tangential to a surface ofrevolution about the turbine axis. In other words, in this outlet endplane, the flow stream returns to being symmetrical about the axis.

These means reduce the tangential static pressure gradient in theneighbourhood of the ceiling plate by a factor λ and/or the tangentialstatic pressure gradient in the neighbourhood of the floor plate by afactor λ', in both cases at the outlet end of the stationary blade set.

To apply the invention to cases where the tangential gradient is dividedby λ the following equation is to be applied: ##EQU20##

All the equations calculated for the curvature of the turbine stagesillustrated in FIGS. 1 to 13 are valid providing the expression in##EQU21## is multiplied by ##EQU22##

To manufacture such a stationary blade set (FIG. 15) in which dp/dt anddp/dr are reduced, extra parts 405 can be placed on the ceiling plate ofthe blade set (other extra parts also being fixed to the floor plate).Each extra part 405 has a contour 403 where it meets the convex surfaceof the blade A and a contour 404 where it meets the concave surface ofthe blade B. The intermediate contour of the part which could have beenused to form the blade sets illustrated in FIGS. 7 to 13 in which nomeans are provided to reduce the secondary losses in the ratio λ or λ'is illustrated in a dashed line.

Means other than hollowing out and adding substance can be used toreduce the tangential static pressure gradient and therefore to reducethe secondary losses of a stationary blade set. Such means are describedfor example in PCT applications published on Apr. 17, 1980 under Nos. WO80/00728 and WO 80/00729.

I claim:
 1. A turbine stage with a circular stationary blade set (204)followed by a circular moving blade set (205), each blade set havingblades (206, 207) mounted between a floor plate and an ceiling platewhich are radially symmetrical about a turbine shaft, the pitch of theblades (206) of the stationary blade in question set being L_(S) at theceiling plate (202) and L_(B) at the floor plate (201, 201') and theoutlet angle of the stream of fluid from the stationary blade set (204)relative to the plane between said blade set (204) being α1_(S) adjacentto the ceiling plate (202) and α1_(B) adjacent to the floor plate (201,201'), in which stage firstly the distance between the turbine shaft andthe surface of the ceiling plate (202, 212) decreases from the inlet endof the stationary blade set (204) to the outlet end of said stationaryblade set (204) where its value is r_(S) then increases from the inletend of the moving blade set (205) where its value is r_(S) up to theoutlet end of the moving blade set (205) and secondly the distancebetween the turbine shaft and the floor plate (201, 211, 201, 211')varies continuously from the inlet side of the stationary blade set(204) to the outlet side of said stationary blade set (204) where itreaches an extreme value r_(B) then varies continously in the oppositedirection from the inlet side of the moving blade set (205) where itsvalue r_(B) up to the outlet of the moving blade set (205),characterized in that the curvature of the meridian line of the ceilingplate (202) of the stationary blade set (204) at the level of the planebetween blade sets is substantially equal to ##EQU23## and in that thecurvature of the meridian line of the floor plate (201, 201') of thestationary blade set (204) adjacent to the plane between the blade setsis substantially equal to difference ##EQU24## the extreme value r_(B)being a minimum when the difference is negative and a maximum when thedifference is positive.
 2. A turbine stage with a circular stationaryblade set (204) followed by a circular moving blade set (205), eachblade set (204, 205) having blades (206, 207) mounted between a floorplate and a ceiling plate which are radially symmetrical about a turbineshaft, the pitch of the blades (206) of the stationary set being L_(S)at the ceiling plate (202) and L_(B) at the floor plate (201, 201') andthe outlet angle of the stream of fluid from the stationary blade set(204) relative to the plane between said blade sets (204) being α1_(S)adjacent to the ceiling plate (202) and α1_(B) adjacent to the floorplate (201, 201'), in which stage firstly the distance between theturbine shaft and the surface of the ceiling plate (202, 212) decreasesfrom the inlet end of the stationary blade set (204) to the outlet endof said stationary blade set (204) where its value is r_(S) then itincreases from the inlet end of the moving blade set (205) where itsvalue is r_(S) up to the outlet end of the moving blade set (205) andsecondly the distance between the turbine shaft and the floor plate(201, 211, 201', 211') varies continuously from the inlet side of thestationary blade set (204) to the outlet side of said stationary bladeset (204) where it reaches an extreme value r_(B) then variescontinuously in the opposite direction from the inlet of the movingblade set (205) where its value is r_(B) up to the outlet of the movingblade set (205), characterized in that means (403, 404) are provided toreduce the tangential static pressure gradient at the outlet end of thestationary blade set (204) by a factor λ(λ>1) in the neighbourhood ofthe ceiling plate and by a factor λ'(λ'>1) in the neighbourhood of thefloor plate, in that the curvature of the meridian line of the ceilingplate of the stationary blade set perpendicular to the plane between theblade sets is substantially equal to ##EQU25## and in that curvature ofthe meridian line of the floor plate of the stationary blade setperpendicular to the plane between the blade sets is substantially equalto the difference ##EQU26## the extreme value r_(B) being a minimum whenthe difference is negative and a maximum when the difference ispositive.
 3. A turbine stage according to any one of claims 1 and 2,characterized in that the distance between the turbine shaft and thesurface of the ceiling plate varies in a curve which has a maximum atthe inlet end of the stationary blade set and at the outlet of themoving blade set and a minimum in the plane between the blade sets.
 4. Ahigh-output turbine according to claim 2, characterized in that thedistance between the turbine shaft and the surface of the floor plate ofthe stationary blade set varies in a curve which has a maximum or aminimum as the case may be at the inlet end of the stationary blade set.